一个知识点

问题如下：

Which of the following options best reflects the characteristics of the one-factor model?The one-factor model is shown as follows:

$U_i=\alpha_iF+\sqrt{1-\alpha_{{}^i}^2Z_i}$

选项：

A.

Each has a component dependent on one common factor (F) and another component (Z_i). Each Zi is uncorrelated with the other variables.

B.

F and Z_i both have Student's t-distributions or F distributions.

C.

The number of calculations for estimating correlations is equal to C(N,2)

D.

The covariance matrix for a one-factor model may not be positive-semidefinite.

解释：

A is correct.

考点：One-factor Model

解析：每一个Ui中，F是相同的，它是common factor。有区别的是Zi，每个Ui中的Zi是彼此独立的，并服从标准正态分布。

接下来的只需要简单了解即可：单因素模型的协方差矩阵是正半定矩阵（positive-semidefinite matrix)；每个单因素模型的相关性估计，只需要N次计算。